Optimization and acceleration guidance of flight trajectories in a windshear
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Engineering topics
Publications and source records attributed to Miele, A..
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The near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear is studied. The take-off problem is considered with reference to flight in a vertical plane; allowance is made for the presence of a downdraft as well as horizontal shear. It is assumed that the power setting is held at the maximum value and that the aircraft is controlled through the angle of attack. While the shear guidance and the initial aftershear guidance use constant gain coefficients, the final aftershear guidance employs a variable gain coefficient. The results show that the guidance scheme for quasi-steady flight recovery yields a transition from quasi-steady flight to quasi-steady flight which is close to that of the optimal trajectory; it guarantees the restoration of the initial quasi-steady state and has good stability properties.
The performance of constant-alpha, maximum-alpha, constant-velocity, constant-absolute-inclination, constant-climb-rate, and constant-pitch (CP) vertical-plane guidance schemes for aircraft taking off under horizontal-windshear conditions with a downdraft is compared by means of numerical simulations; the results are presented in tables and graphs, and it is found that CP guidance gives the best aircraft survivability. Optimal, gamma-guidance, and simplified-gamma trajectories are then evaluated to improve the performance of CP, and the correct selection of the feedback gain coefficient and the time delay for response to windshear onset is shown to be of great importance for maximizing survivability.
The control (via the angle of attack) of the vertical flight of an aircraft taking off at maximum power in a horizontal wind shear with downdraft is investigated analytically. Optimal trajectories to recover the initial path inclination or to recover quasi-steady flight (the relative values of the velocity, path inclination, and angle of attack) are derived using a Chebyshev approach and shown to be nearly identical in the shear but divergent after the shear. These results are then applied to construct a trajectory-guidance control comprising a variable-gamma guidance scheme for the shear trajectory, a constant-gamma guidance scheme for the immediate postshear trajectory, and a constant-rate-of-climb guidance scheme for the aftershear trajectory. Numerical results demonstrating the near-optimal performance of the control are presented in tables and graphs.
Classical and minimax optimal control problems arising in the study of aeroassisted coplanar orbit transfer from a high planetary orbit to a low one are considered. Attention is given to (1) the minimization of the energy required for the maneuver; (2) minimization of the time integral of the heating rate; (3) minimization of the time of flight during the atmospheric portion of the trajectory; (4) maximization of the time of flight during the atmospheric portion of the trajectory; (5) minimization of the time integral of the path inclination; and (6) minimization of the sum of the squares of the entry and exit path inclinations.
The abort landing problem for flight trajectories in the presence of windshear is considered with reference to flight in a vertical plane. The optimal trajectory (OT) problem is a minimax problem or Chebyshev problem of optimal control which can be converted into a Bolza problem through suitable transformations. Numerical results for several combinations of windshear intensities and initial altitudes are presented. A guidance trajectory (GT) law is implemented in feedback control form, subject to prescribed bounds on the angle of attack and its time derivative. Simplified guidance trajectories (SGT) are then considered, leading to a safe target altitude guidance. Conclusions derived for strong-to-severe windshear conditions include GT and SGT preserving the basic properties of OT, and the peak altitude drop of GT and SGT being less than that of the constant pitch trajectory and the maximum angle-of-attack trajectory.
One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.
This paper is concerned with guidance strategies for near-optimum performance in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. The take-off problem is considered with reference to flight in a vertical plane. First, trajectories for optimum performance in a windshear are determined for different windshear models and different windshear intensities. Use is made of the methods of optimal control theory in conjunction with the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. In this approach, global information on the wind flow field is needed. Then, guidance strategies for near-optimum performance in a windshear are developed, starting from the optimal trajectories. Specifically, three guidance schemes are presented: (1) gamma guidance, based on the relative path inclination; (2) theta guidance, based on the pitch attitude angle; and (3) acceleration guidance, based on the relative acceleration. In this approach, local information on the wind flow field is needed.
The present consideration of takeoff trajectory optimization in eight different fundamental problems involving wind shears assumes that the power setting is held at the maximum value, and that the aircraft is controlled with respect to angle-of-attack. While the first three problems are least-squares ones of the Bolza type, the remaining five are minimax problems of the Chebyshev type which can be converted to Bolza type by means of suitable transformations. All problems are solved on the basis of the dual sequential gradient-restoration algorithm for optimal control problems. The trajectory solutions obtained are superior to constant angle-of-attack trajectories.
In the present treatment of optimal control problems arising in the study of coplanar aeroassisted orbital transfer, the hybrid combination of propulsive parameters in space and aerodynamic maneuvers employing lift modulation in the sensible atmosphere indicates that the optimal energy-viewpoint solution is the grazing trajectory; this trajectory is characterized by favorable values of the peak heating rate and the peak dynamic pressure. Numerical solutions are obtained by means of the sequential gradient restoration algorithm for optimal control problems. It is found that nearly-grazing trajectories yielding the least-square value of the path inclination have desirable characteristics from the standpoints of energy, heating rate, and dynamic pressure.
Guidance strategies for near-optimum performance in a wind shear are examined. The takeoff problem is considered with reference to flight in a vertical plane; the presence of a downdraft is assumed. Trajectories for optimum performance in a wind shear are determined for different wind shear models and intensities. Numerical experiments with the optimum control approach lead to the conclusion that, for weak to moderate shear/downdraft combinations, the optimal trajectory is characterized by a monotonic climb, and for severe shear/downdraft combinations, it is characterized by an initial climb, followed by a nearly horizontal flight, followed by renewed climbing after the aircraft has passed through the shear region. An acceleration guidance scheme based on relative acceleration is presented in both analytical form and feedback control form. Numerical results with this scheme result in trajectories close to the optimum and considerably superior to those arising from alternative guidance schemes.
Guidance schemes for near-optimum performance in wind shear are examined. The presence of a downdraft is assumed in addition to the horizontal shear. The takeoff problem is considered with reference to flight in a vertical plane. Trajectories for optimum performance in a wind shear are determined for different wind shear models and intensities. Methods of optimal control theory are used together with the dual sequential gradient-restoration algorithm for optimal control problems. Guidance schemes for near-optimum performance in a wind shear are developed, starting from optimal trajectories. These are gamma guidance, based on either the absolute of the relative path inclination, and theta guidance, based on the pitch attitude angle. These schemes are evaluated through numerical experiments in order to determine whether the resulting trajectories are sufficiently close to optimum and to compare these trajectories with those arising from alternative guidance schemes.
Optimal flight trajectories were determined in the presence of windshear and guidance schemes were developed for near optimum flight in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. This problem is important in the takeoff and landing of both civilian airplanes and military airplanes and is key to aircraft saftey. The topics covered in reference to takeoff problems are: equations of motion, problem formulation, algorithms, optimal flight trajectories, advanced guidance schemes, simplified guidance schemes, and piloting strategies.
The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.
Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.
Gradient techniques in optimization theory with aerospace applicability
Sequential gradient restoration algorithm for optimal control requiring state, control and parameter to satisfy vector differential equation, initial and final conditions
Combined gradient-restoration algorithm for minimizing functional scalar